During the recent century, some valleys in Western Australia have become heavily industrialised. The industries that operate there emit pollution that can change the level of acidity (measured as pH level) of rainwater that falls in the region. Scientists have long suspected that industrial pollution leads to more acidic rain (rain with lower pH level). Scientists know that before the industrial development of the region, the rainwater falling in that region had an average pH level of 6.3, with standard deviation 0.45. Recently, a study of rainwater collected in the region involved 39 samples of rainwater. The scientists observed a sample mean pH of 6.1. The research question here is: Can scientists conclude that the average pH level for rain in this region is lower now than it was before heavy industry arrived?

In formulating hypotheses for a statistical test of significance, the alternative hypothesis is often

A test of significance on the population mean is

Which of the following is a valid alternative hypothesis when comparing two population means?

In a two-independent sample t-test, which of the following is a conservative approximation for the degrees of freedom?

What does it mean when a 95% confidence for (μ₂ − μ₁) includes zero?